For over a year, a global mystery has been growing: Why are so many governments around the world collapsing amid corruption scandals?

Attention is now focused on South Korea, where the Parliament voted Friday to impeach President Park Geun-hye. The allegations against Ms. Park are unique in their colorful details — a mysterious adviser, Choi Soon-sil, is suspected of having secretly influenced Ms. Park's public speeches and decision-making while also extorting millions from major corporations.

But beneath the salacious specifics, the story is familiar: a corruption scandal rocks a nation, reaching the highest levels of government and provoking a political crisis.

It has been a common tale in recent years. In Brazil, for instance, the so-called carwash scandal implicated much of the country’s governing class and led to the impeachment of former President Dilma Rousseff in August. South Africa seems to be heading in the same direction after it was revealed that President Jacob Zuma misusedpublic funds, prompting calls for his ouster. In 2015, Guatemala’s government collapsed after investigators for the United Nations said that President Otto Pérez Molina and Roxana Baldetti, his vice president, had been involved in a bribery scheme. And in Argentina, former President Cristina Fernández de Kirchner and four officials from her party were indicted in August on corruption charges.

The cavalcade of scandals can make it seem like the world’s politicians have suddenly become greedier en masse.

But focusing on individual wrongdoing is misleading, says Raymond Fisman, a professor of behavioral economics at Boston University who studies systemic corruption, which occurs when the corruption is so widespread and severe that it becomes an integral part of a country’s economic and political life. Once systemic corruption takes hold, he explained, it can quickly infect an entire system, encouraging or even forcing bad behavior — even by those who would, in another context, remain honest.

Seen through that lens, experts say, the recent scandals may in fact be cautiously good news. They show that prosecutors and other institutions have managed to break free of those systems and hold their leaders to account — with overwhelming public support for that accountability when they do.

Dangerous Equilibrium

Professor Fisman argues that the most accurate way to think of corruption is as an “equilibrium” — the result of people acting rationally within a flawed system, not just individual moral lapses.

The cost-benefit analysis of whether to pay a bribe, he explained, "depends on how many people around me I think are also engaged in corruption.”

If most people are honest, he said, paying a bribe is a risky endeavor. There are relatively few people interested in accepting one, and many willing to report bribery to the authorities. In that scenario, the equilibrium favors honest dealing.

But “if everyone around you is paying bribes, the cost-benefit tradeoff flips,” he continued. “As more and more people engage in corruption, you’re better able to find willing partners in crime. And the benefits of staying honest decline, because everybody is cutting in front of you in line to see the doctor, or winning the contracts that you might have had a decent chance of getting.”

A new equilibrium will take hold — one that favors dishonest dealings.

That kind of corrupt equilibrium is the background to South Korea’s current scandal. Although the idiosyncrasies of the accusations against Ms. Park have grabbed global attention, the case is just the latest in a series of major corruption scandals that have erupted in the country.

In 2014, after the Sewol ferry disaster killed 302 people, including 250 high school students, an investigation revealed the ferry owner had colluded with government officials to evade safety checks. In January of this year, Prime Minister Lee Wan-koo resigned in a bribery scandal. And there have also been major scandals involving the chaebols, which are family-owned business conglomerates that hold considerable power in South Korea.

In fact, during her campaign and presidency, Ms. Park had presented herself as someone who could take on that corrupt system. Unmarried and childless, she highlighted her lack of close family as an asset to her presidency because so many previous scandals had involved steering assets to children or spouses. After the Sewol disaster, Ms. Park promised to attack the “layers of corruption” that had contributed to it.

But it now appears that Ms. Choi took advantage of the president’s isolation to gain influence over her and exploit that connection for financial and other benefits. Instead of fighting the country’s layers of corruption, the president now looks very likely to leave office disgraced and tainted by them herself.

In Brazil, the impeachment of Ms. Rousseff drew the most global attention to the corruption crisis there, but the scandal has implicated a large swath of the country’s political and economic elite. Dozens of private businessmen have been indicted or tried for skimming funds from state-owned oil company Petrobras. And at least 50 Brazilian lawmakers are currently under investigation.

Restoring Public Trust

Once a corrupt equilibrium is in place, experts say, it cannot be stopped until public trust in the government’s institutions and leaders is restored. That is why the investigations that have led to scandals in South Korea, Brazil, and elsewhere are so significant.

“When Ray and I say that corruption is an equilibrium, what it really means is that institutions are only strong when you believe in them,” said Miriam Golden, a political scientist at the University of California, Los Angeles, who wrote a new book on corruption with Professor Fisman. “I don’t want to say that our institutions only exist in our minds, but really that’s true. What is the rule of law except that we ultimately believe that we ought to follow certain rules?”

But in corrupt systems that belief is often missing, because the institutions that are supposed to provide accountability are often weakened through bribery, threats, and other illicit means.

“The normal institutions of justice — the courts, the prosecutors, the auditors, the ombudsmen, you name it — are themselves so thoroughly corrupted that you can steal with impunity,” said Matthew C. Stephenson, a professor at Harvard Law School who studies corruption. That batters public trust, and strengthens the perception that corruption is universal and unavoidable.

Democratic checks on public abuses can be weakened the same way, he added. “If the electoral process is sufficiently corrupted that you can buy votes or otherwise manipulate it, then you’re not really concerned about your corruption posing an electoral threat,” he said.

That is the situation in countries like Russia, said Christoph Stefes, a professor of political science at the University of Colorado, Denver, who studies authoritarianism and democratization. In Russia, control over both political power and corruption is concentrated among a small group of politicians and the oligarchs in their inner circle, and no institution or prosecutor has enough power to challenge them.

But when prosecutors or other officials gain enough independence to investigate corrupt officials, that can begin to disrupt the corrupt equilibrium.

“I call them ‘islands of honesty’” Professor Stefes said. Such investigations are not sufficient on their own to eradicate corruption, he said. “But they certainly can make a difference as soon as they start spreading, especially when they can connect with civil society.”

That kind of connection is at the heart of many of the major corruption stories of recent years. In South Korea, prosecutors not only investigated Ms. Choi, they also questioned Ms. Park — the first time a sitting president was subjected to that kind of investigation. And their investigation was bolstered by enormous public support, which included the largest protests in the country’s history.

In Guatemala, a special United Nations commission operating outside the ordinary justice system conducted the investigation that implicated then-President Otto Pérez Molina and Vice President Roxana Baldetti in a major customs fraud. The commission’s evidence prompted large public protests, and both Mr. Pérez Molina and Ms. Baldetti eventually resigned.

In South Africa, public ombudsman Thulisile Madonsela determined that Mr. Zuma had misused public funds to upgrade his private home. The country’s constitutional court ruled that her findings and demands were binding. Mr. Zuma now faces a public inquiry and increasing pressure to resign.

And what about the United States, where President-elect Donald J. Trump has recently come under criticism for his apparent mixing of personal and public business? Until recently, experts have believed that the strong institutions typical of wealthy, developed democracies are a robust protection against systemic corruption.

“I always said that I don’t study the U.S. because it’s not that interesting,” Professor Golden said during a recent interview. “It’s just not that corrupt.”

But since the election of Mr. Trump, she said, that has changed.

Mr. Trump does not seem to accept the standard division between public and private, Professor Golden said, referring to Mr. Trump’s decision to have his children run his business instead of placing his holdings in a blind trust, and his apparent mixing of business meetings and governmental decisions during the transition period.

And yet the response from the public and the Republican Party has been muted.

“Those protections are already not functioning,” Professor Golden said. “The question is how much more seriously they could degenerate.”